Algebra & Number Theory

A $p$-adic Eisenstein measure for vector-weight automorphic forms

Ellen Eischen

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We construct a p-adic Eisenstein measure with values in the space of vector-weight p-adic automorphic forms on certain unitary groups. This measure allows us to p-adically interpolate special values of certain vector-weight C automorphic forms, including Eisenstein series, as their weights vary. This completes a key step toward the construction of certain p-adic L-functions.

We also explain how to extend our methods to the case of Siegel modular forms and how to recover Nicholas Katz’s p-adic families of Eisenstein series for Hilbert modular forms.

Article information

Algebra Number Theory, Volume 8, Number 10 (2014), 2433-2469.

Received: 3 March 2014
Revised: 22 September 2014
Accepted: 3 November 2014
First available in Project Euclid: 20 December 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11F03: Modular and automorphic functions
Secondary: 11F33: Congruences for modular and $p$-adic modular forms [See also 14G20, 22E50] 11F30: Fourier coefficients of automorphic forms 11F55: Other groups and their modular and automorphic forms (several variables) 11F85: $p$-adic theory, local fields [See also 14G20, 22E50] 11F46: Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms

Eisenstein measure $p$-adic modular forms $p$-adic automorphic forms Eisenstein series Siegel modular forms automorphic forms on unitary groups


Eischen, Ellen. A $p$-adic Eisenstein measure for vector-weight automorphic forms. Algebra Number Theory 8 (2014), no. 10, 2433--2469. doi:10.2140/ant.2014.8.2433.

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